Fair prediction with disparate impact: A study of bias in recidivism prediction instruments

Alexandra Chouldechova asks how a risk score can satisfy one statistical fairness requirement while failing another—and how the difference could affect decisions. The February 2017 long manuscript combines an algebraic relationship, a COMPAS reanalysis and hypothetical penalty policies. These contributions distinguish the meaning of a prediction from the consequences of using it.^[1]

Different fairness questions

Calibration across groups asks whether a given score corresponds to the same observed outcome frequency in each group. Predictive parity asks whether people above a chosen high-risk threshold have the same outcome frequency. These are not interchangeable: even calibrated scores can have different mixtures above the threshold. Error-rate balance instead compares false-positive rates among recorded non-recidivists and false-negative rates among recorded recidivists.^[1]

The empirical analysis uses ProPublica’s Broward County data on people scored in 2013–2014, with recorded two-year outcomes. After the reported filtering, it includes 6,150 defendants: 3,696 recorded as African-American and 2,454 as Caucasian. Figure 1 finds approximate calibration and predictive parity at several thresholds alongside unequal error rates. These are properties of the analyzed data and score, not an endorsement of every decision made with COMPAS.^[1]

Why unequal base rates constrain the metrics

Equation 2.6 relates a group’s outcome prevalence p, positive predictive value PPV, and error rates at an operating threshold:

FPR = [p / (1 − p)] × [(1 − PPV) / PPV] × (1 − FNR)

With both outcome classes present, a common predictive value strictly between zero and one, and a common nonzero true-positive rate, different prevalences require different false-positive rates. Predictive parity and both equal error rates cannot all hold under those conditions. Boundary cases matter: zero false positives can give 100% predictive value even while positives are missed; flagging nobody leaves predictive value undefined. This is a conditional constraint, not a claim that every pair of fairness goals always conflicts.^[1]

The manuscript reports observed recidivism of about 51% versus 39% in the two groups. It uses that difference to explain why changing the cutoff cannot simply make all the measured criteria agree. Fairness Tradeoffs supplies definitions and worked arithmetic; Inherent Trade-Offs in the Fair Determination of Risk Scores studies a different combination of score-level requirements.^[1]

A score needs a decision rule

The long manuscript then assumes that a high-risk classification triggers a larger penalty within an allowed range. Under that stated policy, Corollary 3.1 makes the difference in average penalty among recorded non-recidivists equal to the penalty-range width multiplied by the false-positive-rate difference. A larger penalty gap amplifies the burden of classification errors. The printed branches of Equation 3.1 are inconsistent with this stricter-high-risk description; this account follows the prose and subsequent corollary.^[1]

The name MinMax here refers to minimum and maximum penalties, not a decision-theoretic minimax strategy. An additional policy interpolates across scores. The empirical illustrations apply hypothetical sentencing rules modeled on Pennsylvania guidelines to the Broward County records; they are not observations of the sentences those defendants actually received.^[1]

This changes what a metric improvement means. Holding predictive value fixed while equalizing false-positive rates may require increasing false negatives, reducing one group’s burden among non-recidivists while increasing it among recidivists. The paper also considers relaxing predictive parity. It does not select a universally correct tradeoff, and explicitly limits the penalty analysis: a high-risk flag used to offer support has a different consequence.^[1]

The label is part of the evidence

The discussion distinguishes observed recidivism from actual reoffending. Offenses may go undetected, and group differences in detection can distort empirical fairness assessments. The algebra remains a relationship among the measured quantities; it does not establish that the outcome label measures the same underlying behavior equally well in every group.^[1]

Read the investigation entry for the documented dispute. Chouldechova’s contribution is to connect the statistical choice to a specified use: a prediction’s fairness cannot be assessed independently of its label, threshold and consequences.

Historical context

The short conference manuscript was submitted October 24, 2016; the separate long manuscript was submitted February 28, 2017. This account follows the latter’s definitions and penalty analysis without treating the two texts as identical.^[1]